In 1891, the Newman family, built a one-room frame school for their children on a 100 X 100 foot plot of land at Blodgett and Velasco, part of District No. 24. In 1897 the school known as the Newman School was enlarged to accommodate sixty neighborhood students who were the children of primarily prosperous German farmers. The teachers boarded at the Newman residence and traveled home to Houston on Friday afternoons. The school was renamed the Sutton and Newman School honoring the Newman family and William Seneca Sutton who was the Superintendent of Houston Independent Schools from 1887 to 1897. William Sutton also taught at the University of Texas and later served as President of the University of Texas. He died in Austin, Texas in 1928 and was buried in the State Cemetery of Austin.

Early 1900 Harris County expanded the school property and enlarged the school. A three room brick building with a basement was constructed. In 1912 the school was abandoned. District 24 merged with Houston Independent School District. The school children were sent to distant schools in Houston.

In 1927 the Sutton and Newman School grounds and buildings were deeded back to Mrs. Newman as part payment for a larger six acre site on Rosedale Avenue adjoining the original Newman homestead. An updated school with a cafeteria and auditorium was built. The school was named the William S. Sutton School. When the school opened in September of 1929 it had only four teachers. The school grew as Houston spread over the surrounding woods. In the late 1950's school enrollment had increased to over 1600 students.

In 1958 the school was relocated to it's present site in the Sharpstown area of Houston. It was renamed Sutton Elementary School and opened on January 27th. Raymond C. Roebuck was the principal. There were 17 faculty members and 500 students most of whom came from neighboring Braeburn elementary School where they had been attending in temporary buildings.

The enrollment increased to 1,500 students by 1961. In 1964 a large permanent wing (the third wing) had been added and the enrollment increased to 1,645 students. The enrollment expanded to 1,742 children during the 1965-1966 school year.  Enrollment in 2016 stands at 1150 students, with over 100 employees.

After 27 years of service at Sutton Elementary Sarah Cripps-Rains retired and Luis Landa became the principal in February 2016. Dr. Landa served as principal of Sutton for 3 years. Dr. Beatrice Akala was hired in July of 2019 and became principal after serving at Wisdom High School.